Moderation & Mediation
Story - 1
In this story we are looking at effect of watching video games. In this particular dataset we have three variable -
- No. of hours / week used to watch (violent) videos
- Aggression
- Callous Unemotional Trait
Therefore, this story is about examining relationship between aggression and time spent in watching videos.
setwd("E:/Outline/WD/D3.1")
dir()## [1] "aggression.csv"
## [2] "Categorical analysis.csv"
## [3] "Categorical analysis.xlsx"
## [4] "correlation analysis.pdf"
## [5] "Data visualisation - An Overview.Rmd"
## [6] "desire.xlsx"
## [7] "e_stress.csv"
## [8] "Examing Relations.R"
## [9] "frienship.csv"
## [10] "mediation"
## [11] "moderation"
## [12] "Moderation---Mediation.Rmd"
## [13] "Moderation & Mediation.Rmd"
## [14] "path analysis.R"
## [15] "pmi.csv"
## [16] "relation.csv"video <- read.csv("aggression.csv")
str(video)## 'data.frame': 442 obs. of 5 variables:
## $ X : int 1 2 3 4 5 6 7 8 9 10 ...
## $ ID : int 69 55 7 96 130 124 72 139 102 179 ...
## $ Aggress : int 13 38 30 23 25 46 41 22 35 23 ...
## $ Vid_Game: int 16 12 32 10 11 29 23 15 20 20 ...
## $ CaUnTs : int 0 0 0 1 1 1 2 3 3 3 ...summary(video)## X ID Aggress Vid_Game CaUnTs
## Min. : 1.0 Min. : 1.0 Min. : 9.00 Min. : 1.00 Min. : 0.0
## 1st Qu.:111.2 1st Qu.:111.2 1st Qu.:32.00 1st Qu.:17.00 1st Qu.:11.0
## Median :221.5 Median :221.5 Median :40.00 Median :22.00 Median :18.0
## Mean :221.5 Mean :221.5 Mean :40.05 Mean :21.84 Mean :18.6
## 3rd Qu.:331.8 3rd Qu.:331.8 3rd Qu.:48.00 3rd Qu.:26.00 3rd Qu.:26.0
## Max. :442.0 Max. :442.0 Max. :82.00 Max. :38.00 Max. :43.0The variable which are of our interst are Agress, Vi_Game and CaUnTs. So this is a small story which just involves three variables.
plot_ly(data = video,x = ~Vid_Game, y = ~Aggress, color = ~CaUnTs, size = ~CaUnTs, type = "scatter")## No scatter mode specifed:
## Setting the mode to markers
## Read more about this attribute -> https://plot.ly/r/reference/#scatter-mode## Warning: `line.width` does not currently support multiple values.Now , we all know the agression is a behaviour , which depends upon attitude. Now CaUnTs which inplies Casual and Unemotional aspect of the subjects - may be considered as attitude.
I am considering them as the context. In any visalisaion , interplay of variable should be seen in a context.
From the above plot one can note that -
there is section of people represented by “small and blue” dots - for them , watching videos for long hours dont lead to aggressive behavior.
and there is section (represeneted by larger points with green and yellow COLOR) , for them increase in exposure to violent videos lead to increase in aggression.
And to be sure the next plot is drawn.
ggplot(data = video, aes(x = Vid_Game, y = Aggress)) + geom_point(aes(size = CaUnTs, color = CaUnTs)) + facet_grid(cut(video$CaUnTs,4)) + geom_smooth(method = "lm", color = "red")
In this plot (static in nature) we have explored the relation ship between exposure to violent videos and aggression.
Four sub-plots shows , that people having higher CaUnTs (as represented by larges points) shows more aggression as they are exposed to videos.
So the relationship between Agression and No.of hours spent to watch videos(violent) depends upon the value of CaUnTs. This phenomena in statistics is known as “MODERATION”. And we have used to unravel this relationship with the help of visualisaiton.
In the following section we shall see how such relationships should modelled. Let us take only two variables , i.e. no of hours spent to watch violent videoa and second is CaUnTs.
library(psych)## Warning: package 'psych' was built under R version 3.5.3##
## Attaching package: 'psych'## The following objects are masked from 'package:ggplot2':
##
## %+%, alpham1 <- lm(Aggress ~ Vid_Game + CaUnTs, data = video)
summary(m1)##
## Call:
## lm(formula = Aggress ~ Vid_Game + CaUnTs, data = video)
##
## Residuals:
## Min 1Q Median 3Q Max
## -27.952 -6.696 -0.168 7.022 32.499
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 21.76433 1.80731 12.042 < 2e-16 ***
## Vid_Game 0.18769 0.06940 2.705 0.00711 **
## CaUnTs 0.76312 0.05024 15.191 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 10.13 on 439 degrees of freedom
## Multiple R-squared: 0.3559, Adjusted R-squared: 0.353
## F-statistic: 121.3 on 2 and 439 DF, p-value: < 2.2e-16So, R^2 stands at 35.6%. At the same time all the coefficients are significant.
Since , the relationship between agression and no of hours spent to watch video is moderated by the attitude (CaUnTs) - we are considering to inlcude “an interaction term” - which is the product of the two predictors.
video$Interaction = video$Vid_Game * video$CaUnTs
summary(lm(Aggress ~ Vid_Game + CaUnTs + Interaction, data = video))##
## Call:
## lm(formula = Aggress ~ Vid_Game + CaUnTs + Interaction, data = video)
##
## Residuals:
## Min 1Q Median 3Q Max
## -29.7144 -6.9087 -0.1923 6.9036 29.2290
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 33.120233 3.427254 9.664 < 2e-16 ***
## Vid_Game -0.333597 0.150826 -2.212 0.027495 *
## CaUnTs 0.168949 0.161049 1.049 0.294731
## Interaction 0.027062 0.006981 3.877 0.000122 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 9.976 on 438 degrees of freedom
## Multiple R-squared: 0.3773, Adjusted R-squared: 0.373
## F-statistic: 88.46 on 3 and 438 DF, p-value: < 2.2e-16From the summary, we can not that R^2 has increased to 37.7%. Also we can observe the following -
CaUnTs is NO LONGER a significant predictor
Interaction term is signifcant at .1% level.
Vid_Game i.e. hours spent to watch video is signficant at 5%.
Story - 3
The third story is about the study done on moderating role of social ties on entrepreneurs’ depressed affect and withdrawal intentions in response to economic stress by Pollack, J., VanEpps, E. M., & Hayes, A. F. (2012). (The . Journal of Organizational Behavior, 33, 789-810.)
stress <- read.csv("e_stress.csv")
str(stress)## 'data.frame': 262 obs. of 7 variables:
## $ tenure : num 1.67 0.58 0.58 2 5 9 0 2.5 0.5 0.58 ...
## $ estress : num 6 5 5.5 3 4.5 6 5.5 3 5.5 6 ...
## $ affect : num 2.6 1 2.4 1.16 1 1.5 1 1.16 1.33 3 ...
## $ withdraw: num 3 1 3.66 4.66 4.33 3 1 1 2 4 ...
## $ sex : int 1 0 1 1 1 1 0 0 1 1 ...
## $ age : int 51 45 42 50 48 48 51 47 40 43 ...
## $ ese : num 5.33 6.05 5.26 4.35 4.86 5.05 3.66 6.13 5.26 4 ...summary(stress)## tenure estress affect withdraw
## Min. : 0.000 Min. :1.00 Min. :1.000 Min. :1.000
## 1st Qu.: 0.940 1st Qu.:3.50 1st Qu.:1.160 1st Qu.:1.000
## Median : 4.000 Median :4.50 Median :1.330 Median :2.000
## Mean : 5.929 Mean :4.62 Mean :1.598 Mean :2.321
## 3rd Qu.: 8.980 3rd Qu.:5.50 3rd Qu.:1.830 3rd Qu.:3.000
## Max. :33.000 Max. :7.00 Max. :5.000 Max. :7.000
## sex age ese
## Min. :0.0000 Min. :23.00 Min. :2.530
## 1st Qu.:0.0000 1st Qu.:36.00 1st Qu.:5.000
## Median :1.0000 Median :44.00 Median :5.730
## Mean :0.6183 Mean :43.79 Mean :5.607
## 3rd Qu.:1.0000 3rd Qu.:51.00 3rd Qu.:6.330
## Max. :1.0000 Max. :71.00 Max. :7.000Let us first understand the experiment - characters / variables -
estress - economic stress , the main phenomena
ese - economic and social ties (business networking, i.e. no of people respondent physically met on a + talked to over phone and sent an email on Everday day.
affect - depression due to economic stress
withdraw - closing business
tenure - experience in the business
Rest of the variables are demographic variables and self explanatory in nature.
So, the strings of relationships starts with economic stress and ends with withdrawl symptoms.
Let us the exploration beigns -
plot_ly(data = stress) %>% add_pie(values = table(stress$sex), labels = c("female", "male") ) plot_ly(data = stress) %>% add_pie(values = table(cut(stress$age,5)), labels = c("< 32.6", "> 32.6 & <=42.2", ">42.2 & <=51.8", ">51.8 & <=61.4", ">61.4 & <=71"))plot_ly(data = stress) %>% add_pie(values = table(cut(stress$tenure,5)), labels = c("<=6.6 yrs", ">6.6 & <=13.2 yrs", ">13.2 & <=19.2 yrs", ">19.8 & <= 26.4 yrs" , "> 26.4 & <= 33"))Demographic profile -
Gender profile - 62% male and 38% female
Age profile - 30% of respondetns belongs age range 42 to 52; appraox 28% belongs to 32 to 42. 17% belong to lesst 32 years
Tenure profile - 68% respondents have less than 6.6 years of experience and 20% has expereince of greater than 6.6 and less than 13.2 years. So this two groups constitutes almost 88% of the population.
Now, we shall explore some relationship among the variables, following variables are closely related -
estress
withdraw
affect
library(ppcor)## Warning: package 'ppcor' was built under R version 3.5.3p_cor <- pcor(stress)
cor_est <- p_cor$estimate
cor_est<- as.data.frame(cor_est)
plot_ly(data = cor_est, x = rownames(cor_est), y = colnames(cor_est), z = as.matrix(cor_est), colours = "RdBu") %>% add_heatmap()## Warning: 'heatmap' objects don't have these attributes: 'colours'
## Valid attributes include:
## 'type', 'visible', 'opacity', 'name', 'uid', 'ids', 'customdata', 'meta', 'hoverinfo', 'hoverlabel', 'stream', 'transforms', 'uirevision', 'z', 'x', 'x0', 'dx', 'y', 'y0', 'dy', 'text', 'hovertext', 'transpose', 'xtype', 'ytype', 'zsmooth', 'connectgaps', 'xgap', 'ygap', 'zhoverformat', 'hovertemplate', 'zauto', 'zmin', 'zmax', 'zmid', 'colorscale', 'autocolorscale', 'reversescale', 'showscale', 'colorbar', 'coloraxis', 'xcalendar', 'ycalendar', 'xaxis', 'yaxis', 'idssrc', 'customdatasrc', 'metasrc', 'hoverinfosrc', 'zsrc', 'xsrc', 'ysrc', 'textsrc', 'hovertextsrc', 'hovertemplatesrc', 'key', 'set', 'frame', 'transforms', '_isNestedKey', '_isSimpleKey', '_isGraticule', '_bbox'From the above correlation diagram that “withdrawal” phenomena is most strongly related with affect (depression),economic stress and ese (business related social ties).
affect (depression) is strongly connected with economic stress.
economic stress (estress) is strongly correlated with affect (depression)
ggplot(data = stress, aes(y = withdraw , x = estress), type = "scatter") + geom_smooth(method = "lm")
ggplot(data = stress, aes(y = withdraw , x = estress), type = "scatter") + geom_smooth(method = "lm") + facet_wrap(stress$sex)
ggplot(data = stress, aes(y = withdraw , x = estress), type = "scatter") + geom_smooth(method = "lm") + facet_wrap(cut(stress$tenure,4))
As expected with increase in economic stress we find that tendency to withdraw increases. Next , we will see whether this relationship is modified by any other variables.
As can be seen that the gender modified the relationship.
Tenure also modifes the relationship.
ggplot(data = stress, aes(y = withdraw , x = ese), type = "scatter") + geom_smooth(method = "lm")
ggplot(data = stress, aes(y = withdraw , x = ese), type = "scatter") + geom_smooth(method = "lm") + facet_wrap(stress$sex) # gender is not modifyig the relation
ggplot(data = stress, aes(y = withdraw , x = ese), type = "scatter") + geom_smooth(method = "lm") + facet_wrap(cut(stress$tenure,4))
as expected / hypothesised , with greater intensity of communication within business network leads to lesser tendency of withdrawal.
Tenure does modfy the relationship , but gender has no significant role.
ggplot(data = stress, aes(y = withdraw , x = affect), type = "scatter") + geom_smooth(method = "lm") 
ggplot(data = stress, aes(y = withdraw , x = affect), type = "scatter") + geom_smooth(method = "lm") + facet_wrap(cut(stress$tenure,4))
In line with the expectation increase in depression will lead higher temdency to withdraw.
The direction of the relationship remains same, when gender is factored into.
library(ppcor)
pcor(stress)## $estimate
## tenure estress affect withdraw sex
## tenure 1.000000000 0.07723098 -0.08668162 -0.001028251 -0.03007565
## estress 0.077230978 1.00000000 0.33358282 -0.108779029 0.13051237
## affect -0.086681616 0.33358282 1.00000000 0.387298163 -0.01014002
## withdraw -0.001028251 -0.10877903 0.38729816 1.000000000 0.05852061
## sex -0.030075653 0.13051237 -0.01014002 0.058520611 1.00000000
## age 0.257049090 0.03219888 -0.01518905 -0.041546676 0.08727015
## ese -0.049415031 -0.09514586 -0.12748255 -0.173581975 0.06583409
## age ese
## tenure 0.25704909 -0.04941503
## estress 0.03219888 -0.09514586
## affect -0.01518905 -0.12748255
## withdraw -0.04154668 -0.17358198
## sex 0.08727015 0.06583409
## age 1.00000000 -0.07836776
## ese -0.07836776 1.00000000
##
## $p.value
## tenure estress affect withdraw sex
## tenure 0.0000000000 2.172345e-01 1.659158e-01 9.869123e-01 0.63129307
## estress 0.2172345473 0.000000e+00 4.267181e-08 8.176633e-02 0.03652582
## affect 0.1659158107 4.267181e-08 0.000000e+00 1.264791e-10 0.87148804
## withdraw 0.9869122785 8.176633e-02 1.264791e-10 0.000000e+00 0.35010557
## sex 0.6312930716 3.652582e-02 8.714880e-01 3.501056e-01 0.00000000
## age 0.0000303237 6.073888e-01 8.085276e-01 5.072771e-01 0.16304914
## ese 0.4302268311 1.281791e-01 4.114384e-02 5.264631e-03 0.29307627
## age ese
## tenure 0.0000303237 0.430226831
## estress 0.6073888166 0.128179069
## affect 0.8085275899 0.041143839
## withdraw 0.5072770936 0.005264631
## sex 0.1630491364 0.293076271
## age 0.0000000000 0.210521405
## ese 0.2105214047 0.000000000
##
## $statistic
## tenure estress affect withdraw sex age
## tenure 0.00000000 1.2369744 -1.3894241 -0.01641986 -0.4804870 4.2474667
## estress 1.23697437 0.0000000 5.6505493 -1.74743114 2.1020953 0.5144416
## affect -1.38942410 5.6505493 0.0000000 6.70820043 -0.1619315 -0.2425777
## withdraw -0.01641986 -1.7474311 6.7082004 0.00000000 0.9361035 -0.6640206
## sex -0.48048703 2.1020953 -0.1619315 0.93610351 0.0000000 1.3989299
## age 4.24746669 0.5144416 -0.2425777 -0.66402055 1.3989299 0.0000000
## ese -0.79005995 -1.5262817 -2.0524797 -2.81460925 1.0535718 -1.2552933
## ese
## tenure -0.790060
## estress -1.526282
## affect -2.052480
## withdraw -2.814609
## sex 1.053572
## age -1.255293
## ese 0.000000
##
## $n
## [1] 262
##
## $gp
## [1] 5
##
## $method
## [1] "pearson"# option -1 #
summary(lm(withdraw ~ estress + ese, data = stress))##
## Call:
## lm(formula = withdraw ~ estress + ese, data = stress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.2173 -1.0154 -0.1840 0.9297 5.2005
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.97852 0.55314 7.193 6.82e-12 ***
## estress 0.02308 0.05345 0.432 0.66627
## ese -0.31459 0.08056 -3.905 0.00012 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.214 on 259 degrees of freedom
## Multiple R-squared: 0.05949, Adjusted R-squared: 0.05222
## F-statistic: 8.191 on 2 and 259 DF, p-value: 0.0003554# Option - 2 #
summary(lm(withdraw ~ estress + ese + estress * ese, data = stress))##
## Call:
## lm(formula = withdraw ~ estress + ese + estress * ese, data = stress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.3804 -1.0368 -0.1641 0.9369 4.9653
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 2.45506 1.81526 1.352 0.177
## estress 0.33165 0.35424 0.936 0.350
## ese -0.05447 0.30600 -0.178 0.859
## estress:ese -0.05296 0.06010 -0.881 0.379
##
## Residual standard error: 1.214 on 258 degrees of freedom
## Multiple R-squared: 0.06231, Adjusted R-squared: 0.05141
## F-statistic: 5.715 on 3 and 258 DF, p-value: 0.0008419# option - 3 #
summary(lm(withdraw ~ affect, data = stress))##
## Call:
## lm(formula = withdraw ~ affect, data = stress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -3.1028 -0.8919 -0.2092 0.8713 2.8713
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.17416 0.17035 6.893 4.13e-11 ***
## affect 0.71772 0.09713 7.389 2.02e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.136 on 260 degrees of freedom
## Multiple R-squared: 0.1735, Adjusted R-squared: 0.1704
## F-statistic: 54.6 on 1 and 260 DF, p-value: 2.02e-12summary(lm(affect ~ ese + estress + ese * estress, data = stress))##
## Call:
## lm(formula = affect ~ ese + estress + ese * estress, data = stress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.4413 -0.4153 -0.1620 0.2817 3.6485
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -1.7265 0.9755 -1.770 0.077952 .
## ese 0.4373 0.1645 2.659 0.008316 **
## estress 0.8546 0.1904 4.489 1.08e-05 ***
## ese:estress -0.1197 0.0323 -3.706 0.000257 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6526 on 258 degrees of freedom
## Multiple R-squared: 0.1961, Adjusted R-squared: 0.1868
## F-statistic: 20.98 on 3 and 258 DF, p-value: 3.391e-12library(psych)
stress$inter1 <- stress$tenure * stress$estress
stress$inter2 <- stress$tenure * stress$ese
mediate("withdraw",c("estress", "ese"), m = "affect", data = stress,plot=T)
##
## Mediation/Moderation Analysis
## Call: mediate(y = "withdraw", x = c("estress", "ese"), m = "affect",
## data = stress, plot = T)
##
## The DV (Y) was withdraw . The IV (X) was estress ese . The mediating variable(s) = affect .
##
## Total effect(c) of estress on withdraw = 0.02 S.E. = 0.05 t = 0.43 df= 260 with p = 0.67
## Direct effect (c') of estress on withdraw removing affect = -0.09 S.E. = 0.54 t = 5.1 df= 258 with p = 6.4e-07
## Indirect effect (ab) of estress on withdraw through affect = 0.11
## Mean bootstrapped indirect effect = 0.11 with standard error = 0.03 Lower CI = 0.06 Upper CI = 0.17
##
## Total effect(c) of ese on withdraw = -0.31 S.E. = 0.08 t = -3.91 df= 260 with p = 0.00012
## Direct effect (c') of ese on withdraw removing affect = -0.21 S.E. = 0.05 t = -1.7 df= 258 with p = 0.09
## Indirect effect (ab) of ese on withdraw through affect = -0.11
## Mean bootstrapped indirect effect = -0.1 with standard error = 0.04 Lower CI = -0.19 Upper CI = -0.03
## R = 0.45 R2 = 0.2 F = 21.96 on 3 and 258 DF p-value: 1.29e-15
##
## To see the longer output, specify short = FALSE in the print statement or ask for the summaryNow the above set of regtession can be structured in the following manner (error term ignored)
withdraw = a1 * ese + a2 * estress + a3 * affect - (equation # 1)
affect = b1 * ese + b2 * estress (equation # 2)
ese = c1 * estress (equation # 3)
Therefore, the above system of equation can be written as follows by substrituting the values of “ese” and “affect”
withdrraw = a1 * c1 * estress + a2 * estress + a3 * (b1 * ese + b2 * estress)
= (a1 * c1 + a2) * estress + a3 * (b1 * c1 * ese + b2* estress)
It can also be noted that as we substitute , we end up multiplying the regression coefficient. This can be considered as “Indirect effect”.
In context of first equation , “a1” is the total effect and (a1 * c1) is the indirect effect. The difference between total effect and indirect effect is “Direct Effect”.
summary(lm(ese ~ estress, data = stress)) # c1 = -0.10##
## Call:
## lm(formula = ese ~ estress, data = stress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -2.9849 -0.6162 0.1238 0.6844 1.6426
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 6.09254 0.19641 31.019 <2e-16 ***
## estress -0.10502 0.04063 -2.585 0.0103 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9345 on 260 degrees of freedom
## Multiple R-squared: 0.02505, Adjusted R-squared: 0.0213
## F-statistic: 6.68 on 1 and 260 DF, p-value: 0.0103summary(lm(affect ~ ese + estress, data = stress)) # b1 = -0.15 , b2 = 0.15##
## Call:
## lm(formula = affect ~ ese + estress, data = stress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0357 -0.3980 -0.1338 0.2047 4.1803
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.71716 0.30462 5.637 4.51e-08 ***
## ese -0.15064 0.04436 -3.396 0.000792 ***
## estress 0.15706 0.02944 5.335 2.08e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6685 on 259 degrees of freedom
## Multiple R-squared: 0.1533, Adjusted R-squared: 0.1468
## F-statistic: 23.45 on 2 and 259 DF, p-value: 4.35e-10summary(lm(affect ~ ese + estress, data = stress))##
## Call:
## lm(formula = affect ~ ese + estress, data = stress)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1.0357 -0.3980 -0.1338 0.2047 4.1803
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.71716 0.30462 5.637 4.51e-08 ***
## ese -0.15064 0.04436 -3.396 0.000792 ***
## estress 0.15706 0.02944 5.335 2.08e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6685 on 259 degrees of freedom
## Multiple R-squared: 0.1533, Adjusted R-squared: 0.1468
## F-statistic: 23.45 on 2 and 259 DF, p-value: 4.35e-10mediate("withdraw",c("estress", "ese"), m = "affect", data = stress,plot=T)
##
## Mediation/Moderation Analysis
## Call: mediate(y = "withdraw", x = c("estress", "ese"), m = "affect",
## data = stress, plot = T)
##
## The DV (Y) was withdraw . The IV (X) was estress ese . The mediating variable(s) = affect .
##
## Total effect(c) of estress on withdraw = 0.02 S.E. = 0.05 t = 0.43 df= 260 with p = 0.67
## Direct effect (c') of estress on withdraw removing affect = -0.09 S.E. = 0.54 t = 5.1 df= 258 with p = 6.4e-07
## Indirect effect (ab) of estress on withdraw through affect = 0.11
## Mean bootstrapped indirect effect = 0.11 with standard error = 0.03 Lower CI = 0.06 Upper CI = 0.17
##
## Total effect(c) of ese on withdraw = -0.31 S.E. = 0.08 t = -3.91 df= 260 with p = 0.00012
## Direct effect (c') of ese on withdraw removing affect = -0.21 S.E. = 0.05 t = -1.7 df= 258 with p = 0.09
## Indirect effect (ab) of ese on withdraw through affect = -0.11
## Mean bootstrapped indirect effect = -0.1 with standard error = 0.04 Lower CI = -0.19 Upper CI = -0.03
## R = 0.45 R2 = 0.2 F = 21.96 on 3 and 258 DF p-value: 1.29e-15
##
## To see the longer output, specify short = FALSE in the print statement or ask for the summary